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| High-order kernels for Riemannian Wavefield Extrapolation | |
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The pseudo-screen solution to equation 13
derives from a fourth-order expansion of the square-root
around and :
k_&& a [1+12( b k_a )^2+ 18( b k_a )^4],
k__0&& a_0[1+12( b_0k_a_0 )^2+ 18( b_0k_a_0 )^4].
If we subtract equations A-16 and A-17, we
obtain the following expression for the wavenumber along the
extrapolation direction :
k_k__0+ (a-a_0)
&+&12[a(b a )^2- a_0(b_0a_0)^2]( k_ )^2
&+&18[a(b a )^4- a_0(b_0a_0)^4]( k_ )^4.
We can make the notations
_1 &=& a(b a )^2- a_0(b_0a_0)^2,
_2 &=& a(b a )^4- a_0(b_0a_0)^4,
therefore equation A-18 can be written as
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(20) |
Using the approximation
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(21) |
we can write
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(22) |
If we make the notations
&=& 12_1^2 ,
&=& _1 ,
&=& 14_2 ,
we obtain the mixed-domain Fourier finite-differences solution to the
one-way wave equation in Riemannian coordinates:
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(23) |
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| High-order kernels for Riemannian Wavefield Extrapolation | |
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Next: Bibliography
Up: Sava and Fomel: Riemannian
Previous: Mixed domain
2008-12-02